Using the Zeldovich dynamics to test expansion schemes
Abstract
We apply to the simple case of the Zeldovich dynamics various expansion schemes which may be used to study gravitational clustering. Using the well-known exact solution of the Zeldovich dynamics we can compare in details the predictions of these various perturbative methods with the exact non-linear result. We find that most systematic expansions fail to recover the decay of the response function into the highly non-linear regime. ``Linear methods'' lead to increasingly fast growth in the highly non-linear regime for higher orders, except for Pade approximants which give a bounded response at any order. ``Non-linear methods'' manage to obtain some damping at one-loop order but they fail at higher orders. We note that, although it recovers the exact Gaussian damping, a resummation performed in the high-k limit is not well justified as the generation of non-linear power does not originate from a finite range of wavenumbers (hence there is no simple separation of scales). No method is able to recover the relaxation of the matter power-spectrum at highly non-linear scales. It is possible to impose in a somewhat ad-hoc fashion a Gaussian cutoff, which agrees with the exact two-point functions for two different times. However, this cutoff is not directly related to the clustering of matter and disappears in exact equal-time statistics. On a quantitative level, we find that on weakly non-linear scales the usual perturbation theory and non-linear schemes to which one adds an ansatz for the response function with such a Gaussian cutoff are the two most efficient methods. We can expect these results to hold for the gravitational dynamics as well (as explicitly checked at one-loop order) since the structure of the equations of motion is identical for both dynamics.Keywords
All Related Versions
This publication has 0 references indexed in Scilit: